WORST_CASE(?, O(n^1))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 186 ms]
(4) CpxRelTRS
(5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(6) CpxRelTRS
(7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxWeightedTrs
(9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(10) CpxTypedWeightedTrs
(11) CompletionProof [UPPER BOUND(ID), 0 ms]
(12) CpxTypedWeightedCompleteTrs
(13) NarrowingProof [BOTH BOUNDS(ID, ID), 27 ms]
(14) CpxTypedWeightedCompleteTrs
(15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
(16) CpxRNTS
(17) InliningProof [UPPER BOUND(ID), 682 ms]
(18) CpxRNTS
(19) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
(20) CpxRNTS
(21) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms]
(22) CpxRNTS
(23) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(24) CpxRNTS
(25) IntTrsBoundProof [UPPER BOUND(ID), 213 ms]
(26) CpxRNTS
(27) IntTrsBoundProof [UPPER BOUND(ID), 75 ms]
(28) CpxRNTS
(29) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(30) CpxRNTS
(31) IntTrsBoundProof [UPPER BOUND(ID), 107 ms]
(32) CpxRNTS
(33) IntTrsBoundProof [UPPER BOUND(ID), 32 ms]
(34) CpxRNTS
(35) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(36) CpxRNTS
(37) IntTrsBoundProof [UPPER BOUND(ID), 142 ms]
(38) CpxRNTS
(39) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
(40) CpxRNTS
(41) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(42) CpxRNTS
(43) IntTrsBoundProof [UPPER BOUND(ID), 52 ms]
(44) CpxRNTS
(45) IntTrsBoundProof [UPPER BOUND(ID), 11 ms]
(46) CpxRNTS
(47) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(48) CpxRNTS
(49) IntTrsBoundProof [UPPER BOUND(ID), 96 ms]
(50) CpxRNTS
(51) IntTrsBoundProof [UPPER BOUND(ID), 32 ms]
(52) CpxRNTS
(53) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(54) CpxRNTS
(55) IntTrsBoundProof [UPPER BOUND(ID), 595 ms]
(56) CpxRNTS
(57) IntTrsBoundProof [UPPER BOUND(ID), 322 ms]
(58) CpxRNTS
(59) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(60) CpxRNTS
(61) IntTrsBoundProof [UPPER BOUND(ID), 409 ms]
(62) CpxRNTS
(63) IntTrsBoundProof [UPPER BOUND(ID), 80 ms]
(64) CpxRNTS
(65) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
(66) CpxRNTS
(67) IntTrsBoundProof [UPPER BOUND(ID), 157 ms]
(68) CpxRNTS
(69) IntTrsBoundProof [UPPER BOUND(ID), 73 ms]
(70) CpxRNTS
(71) FinalProof [FINISHED, 0 ms]
(72) BOUNDS(1, n^1)


----------------------------------------

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   f(X, g(X), Y) -> f(Y, Y, Y)
   g(b) -> c
   b -> c

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(c) -> c
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encArg(cons_b) -> b
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g(x_1) -> g(encArg(x_1))
   encode_b -> b
   encode_c -> c


----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   f(X, g(X), Y) -> f(Y, Y, Y)
   g(b) -> c
   b -> c

The (relative) TRS S consists of the following rules:

   encArg(c) -> c
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encArg(cons_b) -> b
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g(x_1) -> g(encArg(x_1))
   encode_b -> b
   encode_c -> c

Rewrite Strategy: INNERMOST
----------------------------------------

(3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(4)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   f(X, g(X), Y) -> f(Y, Y, Y)
   g(b) -> c
   b -> c

The (relative) TRS S consists of the following rules:

   encArg(c) -> c
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encArg(cons_b) -> b
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g(x_1) -> g(encArg(x_1))
   encode_b -> b
   encode_c -> c

Rewrite Strategy: INNERMOST
----------------------------------------

(5) NonCtorToCtorProof (UPPER BOUND(ID))
transformed non-ctor to ctor-system
----------------------------------------

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   b -> c
   f(X, c_g(X), Y) -> f(Y, Y, Y)
   g(c_b) -> c

The (relative) TRS S consists of the following rules:

   encArg(c) -> c
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encArg(cons_b) -> b
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g(x_1) -> g(encArg(x_1))
   encode_b -> b
   encode_c -> c
   b -> c_b
   g(x0) -> c_g(x0)

Rewrite Strategy: INNERMOST
----------------------------------------

(7) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(8)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1).


The TRS R consists of the following rules:

   b -> c [1]
   f(X, c_g(X), Y) -> f(Y, Y, Y) [1]
   g(c_b) -> c [1]
   encArg(c) -> c [0]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encArg(cons_b) -> b [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   encode_b -> b [0]
   encode_c -> c [0]
   b -> c_b [0]
   g(x0) -> c_g(x0) [0]

Rewrite Strategy: INNERMOST
----------------------------------------

(9) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(10)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   b -> c [1]
   f(X, c_g(X), Y) -> f(Y, Y, Y) [1]
   g(c_b) -> c [1]
   encArg(c) -> c [0]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encArg(cons_b) -> b [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   encode_b -> b [0]
   encode_c -> c [0]
   b -> c_b [0]
   g(x0) -> c_g(x0) [0]

The TRS has the following type information:
b :: c:c_g:c_b:cons_f:cons_g:cons_b
c :: c:c_g:c_b:cons_f:cons_g:cons_b
f :: c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b
c_g :: c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b
g :: c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b
c_b :: c:c_g:c_b:cons_f:cons_g:cons_b
encArg :: c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b
cons_f :: c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b
cons_g :: c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b
cons_b :: c:c_g:c_b:cons_f:cons_g:cons_b
encode_f :: c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b
encode_g :: c:c_g:c_b:cons_f:cons_g:cons_b -> c:c_g:c_b:cons_f:cons_g:cons_b
encode_b :: c:c_g:c_b:cons_f:cons_g:cons_b
encode_c :: c:c_g:c_b:cons_f:cons_g:cons_b

Rewrite Strategy: INNERMOST
----------------------------------------

(11) CompletionProof (UPPER BOUND(ID))
The transformation into a RNTS is sound, since:

(a) The obligation is a constructor system where every type has a constant constructor,

(b) The following defined symbols do not have to be completely defined, as they can never occur inside other defined symbols:
none

(c) The following functions are completely defined:

   f_3
   encArg_1
   encode_f_3
   encode_g_1
   encode_b
   encode_c
   b
   g_1

Due to the following rules being added:

   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1, v2) -> null_encode_f [0]
   encode_g(v0) -> null_encode_g [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   b -> null_b [0]
   g(v0) -> null_g [0]
   f(v0, v1, v2) -> null_f [0]

And the following fresh constants:    null_encArg, null_encode_f, null_encode_g, null_encode_b, null_encode_c, null_b, null_g, null_f

----------------------------------------

(12)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   b -> c [1]
   f(X, c_g(X), Y) -> f(Y, Y, Y) [1]
   g(c_b) -> c [1]
   encArg(c) -> c [0]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encArg(cons_b) -> b [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   encode_b -> b [0]
   encode_c -> c [0]
   b -> c_b [0]
   g(x0) -> c_g(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1, v2) -> null_encode_f [0]
   encode_g(v0) -> null_encode_g [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   b -> null_b [0]
   g(v0) -> null_g [0]
   f(v0, v1, v2) -> null_f [0]

The TRS has the following type information:
b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
c :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
f :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
c_g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
c_b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
encArg :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
cons_f :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
cons_g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
cons_b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
encode_f :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
encode_g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
encode_b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
encode_c :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_encArg :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_encode_f :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_encode_g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_encode_b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_encode_c :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_f :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f

Rewrite Strategy: INNERMOST
----------------------------------------

(13) NarrowingProof (BOTH BOUNDS(ID, ID))
Narrowed the inner basic terms of all right-hand sides by a single narrowing step.
----------------------------------------

(14)
Obligation:
Runtime Complexity Weighted TRS where critical functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   b -> c [1]
   f(X, c_g(X), Y) -> f(Y, Y, Y) [1]
   g(c_b) -> c [1]
   encArg(c) -> c [0]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(c)) -> g(c) [0]
   encArg(cons_g(cons_f(x_161, x_230, x_330))) -> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) [0]
   encArg(cons_g(cons_g(x_162))) -> g(g(encArg(x_162))) [0]
   encArg(cons_g(cons_b)) -> g(b) [0]
   encArg(cons_g(x_1)) -> g(null_encArg) [0]
   encArg(cons_b) -> b [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g(c) -> g(c) [0]
   encode_g(cons_f(x_1125, x_262, x_362)) -> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) [0]
   encode_g(cons_g(x_1126)) -> g(g(encArg(x_1126))) [0]
   encode_g(cons_b) -> g(b) [0]
   encode_g(x_1) -> g(null_encArg) [0]
   encode_b -> b [0]
   encode_c -> c [0]
   b -> c_b [0]
   g(x0) -> c_g(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1, v2) -> null_encode_f [0]
   encode_g(v0) -> null_encode_g [0]
   encode_b -> null_encode_b [0]
   encode_c -> null_encode_c [0]
   b -> null_b [0]
   g(v0) -> null_g [0]
   f(v0, v1, v2) -> null_f [0]

The TRS has the following type information:
b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
c :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
f :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
c_g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
c_b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
encArg :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
cons_f :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
cons_g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
cons_b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
encode_f :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
encode_g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f -> c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
encode_b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
encode_c :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_encArg :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_encode_f :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_encode_g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_encode_b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_encode_c :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_b :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_g :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f
null_f :: c:c_g:c_b:cons_f:cons_g:cons_b:null_encArg:null_encode_f:null_encode_g:null_encode_b:null_encode_c:null_b:null_g:null_f

Rewrite Strategy: INNERMOST
----------------------------------------

(15) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   c => 0
   c_b => 1
   cons_b => 2
   null_encArg => 0
   null_encode_f => 0
   null_encode_g => 0
   null_encode_b => 0
   null_encode_c => 0
   null_b => 0
   null_g => 0
   null_f => 0

----------------------------------------

(16)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(x_162))) :|: x_162 >= 0, z = 1 + (1 + x_162)
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> g(b) :|: z = 1 + 2
   encArg(z) -{ 0 }-> g(0) :|: z = 1 + 0
   encArg(z) -{ 0 }-> g(0) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> b :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_b -{ 0 }-> b :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(x_1126))) :|: x_1126 >= 0, z = 1 + x_1126
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> g(b) :|: z = 2
   encode_g(z) -{ 0 }-> g(0) :|: z = 0
   encode_g(z) -{ 0 }-> g(0) :|: x_1 >= 0, z = x_1
   encode_g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z, z', z'') -{ 1 }-> f(Y, Y, Y) :|: Y >= 0, z'' = Y, z' = 1 + X, X >= 0, z = X
   f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0


----------------------------------------

(17) InliningProof (UPPER BOUND(ID))
Inlined the following terminating rules on right-hand sides where appropriate:

   b -{ 0 }-> 1 :|: 
   b -{ 0 }-> 0 :|: 
   b -{ 1 }-> 0 :|: 
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0

----------------------------------------

(18)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(x_162))) :|: x_162 >= 0, z = 1 + (1 + x_162)
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + x_1, x_1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + x_1, x_1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(x_1126))) :|: x_1126 >= 0, z = 1 + x_1126
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: x_1 >= 0, z = x_1, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: x_1 >= 0, z = x_1, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 1 }-> f(Y, Y, Y) :|: Y >= 0, z'' = Y, z' = 1 + X, X >= 0, z = X
   f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0


----------------------------------------

(19) SimplificationProof (BOTH BOUNDS(ID, ID))
Simplified the RNTS by moving equalities from the constraints into the right-hand sides.
----------------------------------------

(20)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 1 }-> f(z'', z'', z'') :|: z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0


----------------------------------------

(21) CpxRntsAnalysisOrderProof (BOTH BOUNDS(ID, ID))
Found the following analysis order by SCC decomposition:

   { f }
   { b }
   { g }
   { encode_c }
   { encode_b }
   { encArg }
   { encode_g }
   { encode_f }

----------------------------------------

(22)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 1 }-> f(z'', z'', z'') :|: z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {f}, {b}, {g}, {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}

----------------------------------------

(23) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(24)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 1 }-> f(z'', z'', z'') :|: z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {f}, {b}, {g}, {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}

----------------------------------------

(25) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: f
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(26)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 1 }-> f(z'', z'', z'') :|: z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {f}, {b}, {g}, {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: ?, size: O(1) [0]

----------------------------------------

(27) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: f
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(28)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 1 }-> f(z'', z'', z'') :|: z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {b}, {g}, {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]

----------------------------------------

(29) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(30)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {b}, {g}, {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]

----------------------------------------

(31) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: b
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(32)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {b}, {g}, {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: ?, size: O(1) [1]

----------------------------------------

(33) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: b
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(34)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {g}, {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]

----------------------------------------

(35) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(36)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {g}, {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]

----------------------------------------

(37) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

----------------------------------------

(38)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {g}, {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: ?, size: O(n^1) [1 + z]

----------------------------------------

(39) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: g
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(40)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]

----------------------------------------

(41) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(42)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]

----------------------------------------

(43) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_c
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(44)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_c}, {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: ?, size: O(1) [0]

----------------------------------------

(45) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_c
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(46)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]

----------------------------------------

(47) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(48)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]

----------------------------------------

(49) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_b
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(50)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_b}, {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: ?, size: O(1) [1]

----------------------------------------

(51) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_b
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 1

----------------------------------------

(52)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: O(1) [1], size: O(1) [1]

----------------------------------------

(53) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(54)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: O(1) [1], size: O(1) [1]

----------------------------------------

(55) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using KoAT for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: z

----------------------------------------

(56)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encArg}, {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: ?, size: O(n^1) [z]

----------------------------------------

(57) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encArg
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + 2*z

----------------------------------------

(58)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 0 }-> g(g(encArg(z - 2))) :|: z - 2 >= 0
   encArg(z) -{ 0 }-> g(f(encArg(x_161), encArg(x_230), encArg(x_330))) :|: z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 0 }-> f(encArg(z), encArg(z'), encArg(z'')) :|: z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 0 }-> g(g(encArg(z - 1))) :|: z - 1 >= 0
   encode_g(z) -{ 0 }-> g(f(encArg(x_1125), encArg(x_262), encArg(x_362))) :|: x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [1 + 2*z], size: O(n^1) [z]

----------------------------------------

(59) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(60)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 5 + 2*x_161 + 2*x_230 + 2*x_330 }-> s11 :|: s7 >= 0, s7 <= x_161, s8 >= 0, s8 <= x_230, s9 >= 0, s9 <= x_330, s10 >= 0, s10 <= 0, s11 >= 0, s11 <= s10 + 1, z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ -1 + 2*z }-> s14 :|: s12 >= 0, s12 <= z - 2, s13 >= 0, s13 <= s12 + 1, s14 >= 0, s14 <= s13 + 1, z - 2 >= 0
   encArg(z) -{ 4 + 2*x_1 + 2*x_2 + 2*x_3 }-> s2 :|: s' >= 0, s' <= x_1, s'' >= 0, s'' <= x_2, s1 >= 0, s1 <= x_3, s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 4 + 2*z + 2*z' + 2*z'' }-> s6 :|: s3 >= 0, s3 <= z, s4 >= 0, s4 <= z', s5 >= 0, s5 <= z'', s6 >= 0, s6 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 5 + 2*x_1125 + 2*x_262 + 2*x_362 }-> s19 :|: s15 >= 0, s15 <= x_1125, s16 >= 0, s16 <= x_262, s17 >= 0, s17 <= x_362, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18 + 1, x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 1 + 2*z }-> s22 :|: s20 >= 0, s20 <= z - 1, s21 >= 0, s21 <= s20 + 1, s22 >= 0, s22 <= s21 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [1 + 2*z], size: O(n^1) [z]

----------------------------------------

(61) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 1 + z

----------------------------------------

(62)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 5 + 2*x_161 + 2*x_230 + 2*x_330 }-> s11 :|: s7 >= 0, s7 <= x_161, s8 >= 0, s8 <= x_230, s9 >= 0, s9 <= x_330, s10 >= 0, s10 <= 0, s11 >= 0, s11 <= s10 + 1, z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ -1 + 2*z }-> s14 :|: s12 >= 0, s12 <= z - 2, s13 >= 0, s13 <= s12 + 1, s14 >= 0, s14 <= s13 + 1, z - 2 >= 0
   encArg(z) -{ 4 + 2*x_1 + 2*x_2 + 2*x_3 }-> s2 :|: s' >= 0, s' <= x_1, s'' >= 0, s'' <= x_2, s1 >= 0, s1 <= x_3, s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 4 + 2*z + 2*z' + 2*z'' }-> s6 :|: s3 >= 0, s3 <= z, s4 >= 0, s4 <= z', s5 >= 0, s5 <= z'', s6 >= 0, s6 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 5 + 2*x_1125 + 2*x_262 + 2*x_362 }-> s19 :|: s15 >= 0, s15 <= x_1125, s16 >= 0, s16 <= x_262, s17 >= 0, s17 <= x_362, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18 + 1, x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 1 + 2*z }-> s22 :|: s20 >= 0, s20 <= z - 1, s21 >= 0, s21 <= s20 + 1, s22 >= 0, s22 <= s21 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_g}, {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [1 + 2*z], size: O(n^1) [z]
  encode_g: runtime: ?, size: O(n^1) [1 + z]

----------------------------------------

(63) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_g
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 3 + 2*z

----------------------------------------

(64)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 5 + 2*x_161 + 2*x_230 + 2*x_330 }-> s11 :|: s7 >= 0, s7 <= x_161, s8 >= 0, s8 <= x_230, s9 >= 0, s9 <= x_330, s10 >= 0, s10 <= 0, s11 >= 0, s11 <= s10 + 1, z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ -1 + 2*z }-> s14 :|: s12 >= 0, s12 <= z - 2, s13 >= 0, s13 <= s12 + 1, s14 >= 0, s14 <= s13 + 1, z - 2 >= 0
   encArg(z) -{ 4 + 2*x_1 + 2*x_2 + 2*x_3 }-> s2 :|: s' >= 0, s' <= x_1, s'' >= 0, s'' <= x_2, s1 >= 0, s1 <= x_3, s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 4 + 2*z + 2*z' + 2*z'' }-> s6 :|: s3 >= 0, s3 <= z, s4 >= 0, s4 <= z', s5 >= 0, s5 <= z'', s6 >= 0, s6 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 5 + 2*x_1125 + 2*x_262 + 2*x_362 }-> s19 :|: s15 >= 0, s15 <= x_1125, s16 >= 0, s16 <= x_262, s17 >= 0, s17 <= x_362, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18 + 1, x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 1 + 2*z }-> s22 :|: s20 >= 0, s20 <= z - 1, s21 >= 0, s21 <= s20 + 1, s22 >= 0, s22 <= s21 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [1 + 2*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [3 + 2*z], size: O(n^1) [1 + z]

----------------------------------------

(65) ResultPropagationProof (UPPER BOUND(ID))
Applied inner abstraction using the recently inferred runtime/size bounds where possible.
----------------------------------------

(66)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 5 + 2*x_161 + 2*x_230 + 2*x_330 }-> s11 :|: s7 >= 0, s7 <= x_161, s8 >= 0, s8 <= x_230, s9 >= 0, s9 <= x_330, s10 >= 0, s10 <= 0, s11 >= 0, s11 <= s10 + 1, z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ -1 + 2*z }-> s14 :|: s12 >= 0, s12 <= z - 2, s13 >= 0, s13 <= s12 + 1, s14 >= 0, s14 <= s13 + 1, z - 2 >= 0
   encArg(z) -{ 4 + 2*x_1 + 2*x_2 + 2*x_3 }-> s2 :|: s' >= 0, s' <= x_1, s'' >= 0, s'' <= x_2, s1 >= 0, s1 <= x_3, s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 4 + 2*z + 2*z' + 2*z'' }-> s6 :|: s3 >= 0, s3 <= z, s4 >= 0, s4 <= z', s5 >= 0, s5 <= z'', s6 >= 0, s6 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 5 + 2*x_1125 + 2*x_262 + 2*x_362 }-> s19 :|: s15 >= 0, s15 <= x_1125, s16 >= 0, s16 <= x_262, s17 >= 0, s17 <= x_362, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18 + 1, x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 1 + 2*z }-> s22 :|: s20 >= 0, s20 <= z - 1, s21 >= 0, s21 <= s20 + 1, s22 >= 0, s22 <= s21 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [1 + 2*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [3 + 2*z], size: O(n^1) [1 + z]

----------------------------------------

(67) IntTrsBoundProof (UPPER BOUND(ID))

Computed SIZE bound using CoFloCo for: encode_f
after applying outer abstraction to obtain an ITS,
resulting in: O(1) with polynomial bound: 0

----------------------------------------

(68)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 5 + 2*x_161 + 2*x_230 + 2*x_330 }-> s11 :|: s7 >= 0, s7 <= x_161, s8 >= 0, s8 <= x_230, s9 >= 0, s9 <= x_330, s10 >= 0, s10 <= 0, s11 >= 0, s11 <= s10 + 1, z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ -1 + 2*z }-> s14 :|: s12 >= 0, s12 <= z - 2, s13 >= 0, s13 <= s12 + 1, s14 >= 0, s14 <= s13 + 1, z - 2 >= 0
   encArg(z) -{ 4 + 2*x_1 + 2*x_2 + 2*x_3 }-> s2 :|: s' >= 0, s' <= x_1, s'' >= 0, s'' <= x_2, s1 >= 0, s1 <= x_3, s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 4 + 2*z + 2*z' + 2*z'' }-> s6 :|: s3 >= 0, s3 <= z, s4 >= 0, s4 <= z', s5 >= 0, s5 <= z'', s6 >= 0, s6 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 5 + 2*x_1125 + 2*x_262 + 2*x_362 }-> s19 :|: s15 >= 0, s15 <= x_1125, s16 >= 0, s16 <= x_262, s17 >= 0, s17 <= x_362, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18 + 1, x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 1 + 2*z }-> s22 :|: s20 >= 0, s20 <= z - 1, s21 >= 0, s21 <= s20 + 1, s22 >= 0, s22 <= s21 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: {encode_f}
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [1 + 2*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [3 + 2*z], size: O(n^1) [1 + z]
  encode_f: runtime: ?, size: O(1) [0]

----------------------------------------

(69) IntTrsBoundProof (UPPER BOUND(ID))

Computed RUNTIME bound using CoFloCo for: encode_f
after applying outer abstraction to obtain an ITS,
resulting in: O(n^1) with polynomial bound: 4 + 2*z + 2*z' + 2*z''

----------------------------------------

(70)
Obligation:
Complexity RNTS consisting of the following rules:

   b -{ 0 }-> 1 :|: 
   b -{ 1 }-> 0 :|: 
   b -{ 0 }-> 0 :|: 
   encArg(z) -{ 5 + 2*x_161 + 2*x_230 + 2*x_330 }-> s11 :|: s7 >= 0, s7 <= x_161, s8 >= 0, s8 <= x_230, s9 >= 0, s9 <= x_330, s10 >= 0, s10 <= 0, s11 >= 0, s11 <= s10 + 1, z = 1 + (1 + x_161 + x_230 + x_330), x_330 >= 0, x_161 >= 0, x_230 >= 0
   encArg(z) -{ -1 + 2*z }-> s14 :|: s12 >= 0, s12 <= z - 2, s13 >= 0, s13 <= s12 + 1, s14 >= 0, s14 <= s13 + 1, z - 2 >= 0
   encArg(z) -{ 4 + 2*x_1 + 2*x_2 + 2*x_3 }-> s2 :|: s' >= 0, s' <= x_1, s'' >= 0, s'' <= x_2, s1 >= 0, s1 <= x_3, s2 >= 0, s2 <= 0, x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 1 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 0
   encArg(z) -{ 0 }-> 0 :|: z >= 0
   encArg(z) -{ 0 }-> 0 :|: z = 2
   encArg(z) -{ 1 }-> 0 :|: z = 2
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 0, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 0 :|: z - 1 >= 0, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, 1 = 1
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 1 = v0
   encArg(z) -{ 0 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 1 }-> 0 :|: z = 1 + 2, v0 >= 0, 0 = v0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z - 1 >= 0, 0 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 1 = x0, x0 >= 0
   encArg(z) -{ 0 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encArg(z) -{ 1 }-> 1 + x0 :|: z = 1 + 2, 0 = x0, x0 >= 0
   encode_b -{ 0 }-> 1 :|: 
   encode_b -{ 0 }-> 0 :|: 
   encode_b -{ 1 }-> 0 :|: 
   encode_c -{ 0 }-> 0 :|: 
   encode_f(z, z', z'') -{ 4 + 2*z + 2*z' + 2*z'' }-> s6 :|: s3 >= 0, s3 <= z, s4 >= 0, s4 <= z', s5 >= 0, s5 <= z'', s6 >= 0, s6 <= 0, z >= 0, z'' >= 0, z' >= 0
   encode_f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   encode_g(z) -{ 5 + 2*x_1125 + 2*x_262 + 2*x_362 }-> s19 :|: s15 >= 0, s15 <= x_1125, s16 >= 0, s16 <= x_262, s17 >= 0, s17 <= x_362, s18 >= 0, s18 <= 0, s19 >= 0, s19 <= s18 + 1, x_362 >= 0, z = 1 + x_1125 + x_262 + x_362, x_1125 >= 0, x_262 >= 0
   encode_g(z) -{ 1 + 2*z }-> s22 :|: s20 >= 0, s20 <= z - 1, s21 >= 0, s21 <= s20 + 1, s22 >= 0, s22 <= s21 + 1, z - 1 >= 0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0
   encode_g(z) -{ 0 }-> 0 :|: z = 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 0 :|: z >= 0, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, 1 = 1
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 1 = v0
   encode_g(z) -{ 0 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 1 }-> 0 :|: z = 2, v0 >= 0, 0 = v0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z >= 0, 0 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 1 = x0, x0 >= 0
   encode_g(z) -{ 0 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   encode_g(z) -{ 1 }-> 1 + x0 :|: z = 2, 0 = x0, x0 >= 0
   f(z, z', z'') -{ 2 }-> s :|: s >= 0, s <= 0, z'' >= 0, z' - 1 >= 0, z = z' - 1
   f(z, z', z'') -{ 0 }-> 0 :|: z >= 0, z' >= 0, z'' >= 0
   g(z) -{ 1 }-> 0 :|: z = 1
   g(z) -{ 0 }-> 0 :|: z >= 0
   g(z) -{ 0 }-> 1 + z :|: z >= 0

Function symbols to be analyzed: 
Previous analysis results are:
  f: runtime: O(1) [1], size: O(1) [0]
  b: runtime: O(1) [1], size: O(1) [1]
  g: runtime: O(1) [1], size: O(n^1) [1 + z]
  encode_c: runtime: O(1) [0], size: O(1) [0]
  encode_b: runtime: O(1) [1], size: O(1) [1]
  encArg: runtime: O(n^1) [1 + 2*z], size: O(n^1) [z]
  encode_g: runtime: O(n^1) [3 + 2*z], size: O(n^1) [1 + z]
  encode_f: runtime: O(n^1) [4 + 2*z + 2*z' + 2*z''], size: O(1) [0]

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(71) FinalProof (FINISHED)
Computed overall runtime complexity
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(72)
BOUNDS(1, n^1)